Given $ m \angle LOM = 9x + 44$, $ m \angle MON = 6x + 3$, and $ m \angle LON = 77$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {9x + 44} + {6x + 3} = {77}$ Combine like terms: $ 15x + 47 = 77$ Subtract $47$ from both sides: $ 15x = 30$ Divide both sides by $15$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 6({2}) + 3$ Simplify: $ {m\angle MON = 12 + 3}$ So ${m\angle MON = 15}$.